OK, just the ones that I have thought of while reading this thread:
Jimi Hendrix's cover of Day Tripper
Metallica's Four Horsemen (another Cliff Burton fan here)
Our Lady Peace's Naveed (not that it was terribly proficient, but it was catchy)
Silverchair's Isreal's Son
Bobby Hebb's Sunny
Big Sugar's Diggin' a Hole